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We discuss cosmology based on the cuscuton gravity theory to resolve theanomaly of the observational $^4$He abundance reported by the EMPRESScollaboration. We find that the gravitational constant $G_{\rm cos}$ inFriedmann equation should be smaller than the Newton's constant ${G_{\rm N}}$such that ${\Delta G_{\rm N}}/{G_{\rm N}} \equiv (G_{\rm cos}-G_{\rmN})/{G_{\rm N}} = -0.085_{-0.028}^{+0.026} \quad(68 \% \text { C.L. })$ interms of big-bang nucleosynthesis, which excludes ${\Delta G_{\rm N}}=0$ atmore than 95~$\% \text { C.L. }$ To fit the data, we obtain a negative masssquared of a non-dynamical scalar field with the Planck-mass scale as $\sim -{\mathcal{O}}(1) {M_{\rm PL}^2} ({\mu}/{0.5 M_{\rm PL}})^{4}$ with the cuscutonmass parameter $\mu$. This fact could suggest the need for modified gravitytheories such as the cuscuton gravity theory with a quadratic potential, whichcan be regarded as the low-energy Ho\v{r}ava-Lifshitz gravity and might give ahint of quantum gravity.

A Possible Solution to the Helium Anomaly of EMPRESS VIII by Cuscuton Gravity Theory